Kukushkin won 6-3, 7-6 (4) against the 18-year-old Sinner, who is ranked a career-high 127th after coming through qualifying to reach the U.S. Open main draw. Kukushkin will play either Janko Tipsarevic or Damir Dzumhur in the second round.
Sinner twice came back from a break down in the second set before losing on the tiebreak. France's Mannarino overcame a 4-1 deficit in the first set to win 7-5, 6-2 against Italian Stefano Travaglia. His reward is a second-round meeting with one of two qualifiers, either Lukas Rosol or Egor Gerasimov.
The tournament's highest-seeded players, including No. 1 Daniil Medvedev, have a bye into the second round.
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